Soap film realization of isoperimetric surfaces with boundary

Abstract

We examine surfaces of the type proved to be minimizing under a connectivity condition by Dorff et al. We determine which of these surfaces are stable soap films. The connectivity condition is shown to be very restrictive; few of these surfaces are stable (locally minimizing) without it. 2. The surfaces of Dorff et al. Equitent surfaces are constructed via the union of sections of spheres and planes. Starting with a cone over a wire-frame polyhedron, the center of the cone is then MSC2010: primary 49Q10; secondary 49Q05, 53A10.